2
vINrx are the covariance matrices of the desired transmitted signal, the SI and the noise, respectively.
The MMSE receive filter can be obtained from (2.49) by finding a derivative of the trace of M with respect to wM M SE and equalize the results to zero, i.e. ∂w∂tr{M}M M SE = 0, which yields
wM M SE = HRsoHH(HRsoHH+ HLIRsiHHLI + Rv)−1. (2.50)
After determining the MMSE filter coefficients using (2.50), wM M SE can be applied to the received signal r in order to obtain an estimate of the signal of interest ˆso after minimising the effect of SI as
ˆso = wM M SEr. (2.51)
It is noteworthy that the knowledge of the covariance matrices along with the channels of SI and the desired signal are required to implement this MMSE filter in order to tackle SI in the digital domain. Moreover, scaling needs to be applied to (2.50) in order to satisfy kwM M SEk2F = Nrx[9].
2.6
Chapter Summary
In this chapter, the background and theory of multiple antenna transmission for wireless communication has been investigated and discussed. Different techniques in this area have been described and analysed such as spatial multiplexing, precoding and diversity coding. Furthermore, different equalization and detection techniques have been presented for the sake of recovering the desired signal after passing through MIMO channels. More- over, the fundamentals and challenges of utilizing in-band FD transmission for wireless communication have been discussed, in which the most promising techniques exploited to mitigate the SI associated with FD operation have been outlined and discussed in more detail and for different stages of signal processing, such as the passive suppression in the RF domain and active cancellation in the analogue and digital domains, i.e. before and after the ADC, respectively.
Chapter 3
Performance Analysis of
3.1 Introduction
3.1
Introduction
Due to the continually increasing demands on frequency and energy resources, FD has become an essential necessity and inevitable evolutionary step for the next generation of wireless communications, the fifth generation (5G). FD transceivers allow transmission simultaneously over the same frequency bands. This makes the need for applying SIC methods essential to tackle the SI accompanied with FD operation and obtain the optimum performance of FD.
This chapter focuses on FD-MIMO based relays, over which the source and destina- tion nodes are communicating. In general, the relay has the ability to receive data from the source and deliver it to the destination either by using AF, DF or by EF approaches. Fig. 3.1 illustrates a FD wireless communication via a relay, in which the source (S) communicates with the destination (D) by utilizing the relay (R). Moreover, the notations Hsr, Hrd, andHsd are to represent the channels of the source to relay, the relay to des- tination and the source to destination, respectively. WhileHrris the SI channel between the relay’s output and input.
For these types of relaying, estimation and subtraction operations of SI are required to maximize the SINR, which increases the capacity, improves the overall spectral efficiency and enhances the entire performance of these systems utilizing the FD technique.
Spatial suppression schemes for FD-MIMO transceivers, such as ZF and NSP, are proposed as SIC via exploiting the spatial domain MIMO signal characteristics of the interfering channels. This can be achieved by designing spatial filters via utilizing matrix conversion approaches, as SVD of the SI channel required to suppress the SI [8, 9, 20, 29,
R
H
sdH
rdH
rrS
D
H
sr3.1 Introduction
38].
In contrast, in order to increase the signal-to-noise ratio (SNR), spatial diversity can be exploited for MIMO systems to obtain the full diversity gain available, which can be achieved by utilizing MRC. This approach has been launched and deployed successfully for MIMO systems that operate in the presence of AWGN and interference environments. The MIMO-MRC system may be constructed by introducing transmit and receive beam- forming weight vectors. The selection of beamforming weight vectors can be optimized to satisfy transmitting the signal over the strongest path of the channel. This implies that transmitting the signal along the direction of the eigenvector associated to the largest eigenvalue of the Wishart matrix of a channelH, i.e. HHH [51, 52]. However, perfect CSI is required by the transmitter and receiver in order to obtain better performance.
In this chapter, the works in [8, 9, 20, 29, 38] are extended by combining MRC with NSP for FD-MIMO based relaying in order to maximize the SINR. Additionally, the performance analysis of the proposed system is derived for different performance metrics and in the presence of perfect and imperfect channel estimation. Furthermore, the works in [3, 13, 30, 31] are extended by utilizing EF relaying instead of DF and AF relays, and the relay transformation coefficients are derived for FD-MRC-MIMO using EF relaying in order to minimize the mean square error (MSE) between the transmitted and received symbols. Moreover, the E2E performance is demonstrated using the outage probability, ASER vs. SINR, and capacity performance metrics.
The key contributions of this chapter can be summarized as follows. Firstly, NSP and MRC are exploited jointly in order to mitigate the SI of the undesired loop path and to increase the SNR of the source-to-destination path. The motivation to use MRC-MIMO, which is selected over Full-MIMO, is due to the SNR advantage inherent in transmit and receive beamforming to achieve full diversity gain in such an interference limited envi- ronment. NSP is implemented via utilizing SVD of the CSI of the SI channel. Secondly, the E2E performance analysis of the modelled system takes into account the impact of imperfectly estimated CSI for both the desired and interference channels. Finally, the E2E upper bound mutual information of the proposed FD-MRC-MIMO is derived in the presence of SI. To the best of our knowledge, these aspects have not been thoroughly in- vestigated in previously published research papers. The ideas, derivations and numerical results presented in this chapter are valid for flat fading channels. However, the latter con- dition can be always satisfied by introducing OFDM to combat ISI. As long as a cyclic prefix of sufficient length is selected to cover the delay spread of the multipath channel